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Gaussian Pyramid. Slides from Alexei Efros. Sampling. Good sampling: Sample often or, Sample wisely. Bad sampling: see aliasing in action!. Gaussian pre-filtering. G 1/8. G 1/4. Gaussian 1/2. Solution: filter the image, then subsample

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gaussian pyramid

Gaussian Pyramid

Slides from Alexei Efros

sampling
Sampling
  • Good sampling:
  • Sample often or,
  • Sample wisely
  • Bad sampling:
  • see aliasing in action!
gaussian pre filtering
Gaussian pre-filtering

G 1/8

G 1/4

Gaussian 1/2

  • Solution: filter the image, then subsample
    • Filter size should double for each ½ size reduction. Why?
subsampling with gaussian pre filtering
Subsampling with Gaussian pre-filtering

Gaussian 1/2

G 1/4

G 1/8

  • Solution: filter the image, then subsample
    • Filter size should double for each ½ size reduction. Why?
    • How can we speed this up?
compare with
Compare with...

1/2

1/4 (2x zoom)

1/8 (4x zoom)

Why does this look so crufty?

image pyramids
Image Pyramids
  • Known as a Gaussian Pyramid [Burt and Adelson, 1983]
    • In computer graphics, a mip map [Williams, 1983]
    • A precursor to wavelet transform
slide7

A bar in the big images is a hair on the zebra’s nose; in smaller images, a stripe; in the smallest, the animal’s nose

Figure from David Forsyth

gaussian pyramid construction
Gaussian pyramid construction

filter mask

  • Repeat
    • Filter
    • Subsample
  • Until minimum resolution reached
    • can specify desired number of levels (e.g., 3-level pyramid)
  • The whole pyramid is only 4/3 the size of the original image!
gaussian pyramid construction9
Gaussian pyramid construction

is similar to Gaussian

laplacian pyramid
Laplacian Pyramid

Gaussian Pyramid

  • Laplacian Pyramid decomposition
  • Created from Gaussian pyramid by subtraction
laplacian pyramid11
Laplacian Pyramid

Gaussian Pyramid

  • Laplacian Pyramid decomposition
  • Created from Gaussian pyramid by subtraction
what are they good for
What are they good for?
  • Improve Search
    • Search over translations
      • Like homework
      • Classic coarse-to-fine stategy
    • Search over scale
      • Template matching
      • E.g. find a face at different scales
  • Precomputation
    • Need to access image at different blur levels
    • Useful for texture mapping at different resolutions (called mip-mapping)
  • Image Processing
    • Editing frequency bands separetly
    • E.g. image blending… next time!